1. Field of the Invention
This invention relates generally to spectrum analysis and, more particularly, to analysis by discrete-time filtering.
2. Description of the Prior Art
In many applications of spectral analysis, it is necessary to detect the presence of a signal in a particular band of frequencies and, particularly for a single tone signal, to estimate the frequency of the tone. This is generally accomplished in conventional analog systems by employing an analog filter bank or a single filter which is swept across the frequencies of interest. Associated with such techniques, however, are the usual problems of analog processors, including unpredictability due to inherent variability of system components, as well as the complexities involved with narrowband low-pass or bandpass filter designs.
In the digital domain, a discrete-time technique for partitioning the given frequency bands into subbands for detection purposes is described in companion references. The first is a letter by V. Cappellini entitled "Digital Filtering With Sampled Signal Spectrum Frequency Shift," published in the Proceedings of the IEEE, February, 1969, pages 241 and 242. The other reference is an article by V. Cappellini et al entitled "A Special-Purpose On-Line Processor for Bandpass Analysis," appearing in the IEEE Transactions on Audio and Electroacoustics, June, 1970, pages 188-194. The foundational concept disclosed by these references is the ability to achieve narrowband filtering by frequency-domain spectrum shifting (via time domain operations) and decimation to generate resolution capability within the frequency domain. In accordance with the technique of the references, the input signal (bandlimited to .omega..sub.m) is sampled at the frequency 2.omega..sub.m so as to alias the baseband -.omega..sub.m -to-0 signal into the band .omega..sub.m to 2.omega..sub.m and the sampled signal is processed in two parallel paths. In one path, the sampled signal is filtered with a time-shared, low-pass filter having an initial cutoff frequency of .omega..sub.m /2, thereby developing a signal representation of the input signal's spectrum from 0 to .omega..sub.m /2. In the other path, the sampled signal is shifted in frequency by .omega..sub.m by multiplying the elements of the sampled sequence by (-1).sup.n, and the shifted signal is filtered with the same low-pass filter, thereby developing a signal representation of the input signal's spectrum from .omega..sub.m /2 to .omega..sub.m. In this manner, the digital signals at the output of the two paths are now bandlimited to .omega..sub.m /2. By reducing the sampling rate or decimating by a factor of 2, this approach can be reapplied to each of the two developed signals to obtain four signals, with each output signal now representing a different quarter of the spectrum of the input signal. In this fashion, with an increased number of decimation stages and time-sharing of a single digital filter, successively narrower bands can be evaluated. Thus, the main advantage of this decimation approach for partitioning a given frequency band into several subbands is that a single, fixed low-pass digital filter is required; bandpass analysis can be achieved efficiently with a unique digital filter having fixed coefficients at each stage of decimation.
In a variety of applications, it is known that the spectrum of interest contains, at most, a single spectral line since the input signal is a tone. When this a priori condition is known to exist, the method of Cappellini et al possesses inherent disadvantages. First, once the initial set of data samples is extracted from the incoming waveform, only this set, or residuals thereof, is processed by the remaining filter stages. If the particular interval of sampling is affected by noise or spurious signals, these effects propagate throughout the succeeding stages of decimation. Moreover, numerous samples must be taken initially because at each stage of decimation, one-half of the samples are being discarded. Filter edge effects, leading to deleterious results, may occur as the frequency resolution increases if the number of samples retained at each stage does not dominate the filter length. Finally, the necessity of frequency shifting at each stage unduly complicates an already complex system.